Remarks on basepoint-freeness thresholds of polarized abelian surfaces

TL;DR

This paper determines the basepoint-freeness threshold for a very general polarized abelian surface over complex numbers and provides the first example with an irrational threshold.

Contribution

It explicitly computes the threshold for general cases and presents the first example of an irrational threshold in polarized abelian surfaces.

Findings

Threshold determined for very general polarized abelian surfaces

First example of an irrational basepoint-freeness threshold

Advances understanding of polarization properties in abelian surfaces

Abstract

We determine the basepoint-freeness threshold of a very general polarized abelian surface over the field of complex numbers. We also give the first example of a polarized abelian surface whose basepoint-freeness threshold is irrational.